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A new two-dimensional locally resonant phononic crystal with microcavity structure is proposed. The acoustic wave band gap characteristics of this new structure are studied using finite element method. At the same time, the corresponding displacement eigenmodes of the band edges of the lowest band gap and the transmission spectrum are calculated. The results proved that phononic crystals with microcavity structure exhibited complete band gaps in low-frequency range. The eigenfrequency of the lower edge of the first gap is lower than no microcavity structure. However, for no microcavity structure type of quadrilateral phononic crystal plate, the second band gap disappeared and the frequency range of the first band gap is relatively narrow. The main reason for appearing low-frequency band gaps is that the proposed phononic crystal introduced the local resonant microcavity structure. This study provides a good support for engineering application such as low-frequency vibration attenuation and noise control.

In recent years, a growing interest has been focused on the study of the propagation of elastic waves in the periodic phononic crystals (PCs) [

In order to promote the application of phononic crystals in the fields of vibration control and noise isolation, obtaining tunable BGs with large bandwidth in the low-frequency domain is significant. In the 2DPCs, a lot of studies on the research of large band gap have been carried out to obtain PC structures with excellent BGs. For example, Lai et al. have studied the PC structure composed of the square lattice of steel cylinders in air background and found that the BGs could be tunable with various microstructures [

Recently, some novel periodic structures with large band gaps are reported. Trabelsi et al. investigated the band properties of a phononic crystal composed of alternating fluid and fluid-saturated porous layers [

In this paper, new band gaps structure composed of square scatter with microcavity structure embedded in a homogeneous matrix is considered. We adopted the finite element method to investigate the variable of the band gaps in low frequency. Different numbers of connection bridge plates and connection forms will be studied to confirm the locally resonant mechanism. Furthermore, microcavity structures with different geometric dimension are studied in this work. Finally, some conclusions are given.

PC structure considered here is a square lattice unit cell which contains a square inclusion and junction plates embedded in a homogeneous matrix. Figures

The cross-section structure of the phononic crystal (a) and the unit cell structure of the phononic crystal (b).

In the present study, to research the band gap characteristics of the proposed 2DPC structure, a lot of computes on the dispersion relations and transmission spectra are performed with the FEM [

For the analysis of the transmission spectra, a finite system must be defined. We consider here the structure being finite in the

In this section, the proposed 2DPCs with microcavity structures will be studied using the finite element software COMSOL. The detailed process can be found in [

Materials properties.

Materials | Density ( |
Young’s modulus ( |
Poisson’s ratio ( |
---|---|---|---|

(Kg/m^{3}) |
Pa | ||

A | 4.08 | 11600 | 0.369 |

B | 0.435 | 1180 | 0.368 |

We observe that bands are contained in the frequency range of 0–500 kHz, in Figure

The dispersion curves of the phononic crystal with microcavity structure (a) and the transmission spectra of the phononic crystal with microcavity (b).

As a comparison, we also compute the gap characteristics of the traditional PC composed of scatter inclusions embedded in the epoxy matrix with full contact, namely, no microcavity structure. Obviously, it is a classic 2DPC structure based on the Bragg scattering mechanism. During the computations, the lattice constant and filling ratio are selected to be the same as those used in Figure

The dispersion curves of the phononic crystal with no microcavity structure (a) and the transmission spectra of the phononic crystal with no microcavity (b).

In order to confirm the physical mechanism for the occurrence of the low-frequency band structures in the proposed PC structure, we compute the eigenmode shapes and displacement vector fields at the edges of the first complete band gap. The results are shown in Figure

Eigenmodes shapes and displacement vector fields of the modes marked in Figures

The dispersion curves of the phononic crystal with three connection plates (a). The dispersion curves of the phononic crystal with two opposite connection plates (b). The dispersion curves of the phononic crystal with two adjacent connection plates (c). The dispersion curves of the phononic crystal with only one connection plate.

From the analysis above, we can conclude that the occurrence of the large band gaps in low frequency is mainly attributed to the existence of the localized resonance modes resulting from the introduction of the four connection bridge plates formed microcavity structures. Since the connection bridge plates play the role of springs linking the square scatter and the matrix, their shape features may influence the band structure remarkably. In the following, we will study the effects of the geometrical parameters on the typical large low-frequency band gaps of the proposed PC structure.

Furthermore, we also investigated the band gaps of microcavity structures with 1, 2, and 3 connection bridge plates to the matrix, respectively. The calculated dispersion curves are shown in Figure

The objective of the following is to investigate the effects of geometric dimension on the low-frequency band gap with microcavity structure. First, we investigate the influence of the length of the connection bridge plates on the band gap. Keeping the lattice constant

The dispersion curves of the phononic crystals with different length of connection plates structures.

Second, we investigate the influence of the width of connection plates on the band structure. Figure

The evolution of the band gap as a function of the width of the connection plate

Finally, we also research the effect of the density of the connection plates on the band gaps. Figure ^{3}, the widths of the first and the second band gap vary slightly, while the width of the third band gap rises rapidly. For the first and second band gap, with the increase of the density of the connection plate, the stiffness of the connection plates in the mass-spring system increases rapidly, while the mass of the resonator has no change, resulting in the resonance frequency minor declining accordingly.

The evolution of the band gap as a function of the density of the connection plate.

In this paper, the band structures of two-dimensional PCs with the microcavity structure are investigated using FEM. From these PC structures, a complete band gap can be obtained. The band gap is notably lowered, as expected. The microcavity structure formed with four connection plates bridge to the resonator possess many locally resonators lead to a low-frequency band gap. The displacement fields of eigenmodes are studied to reveal the physical mechanism for the existence of material’s periodic arrangement on the low-frequency band gaps. It was shown that the influence of the geometric dimension and connection plate adjacent shape is much higher than the influence of the materials properties. This provides a more important design factor in engineering application.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors are grateful to the support from the National Science Foundation of China (no. 51175097) and the Zhejiang Provincial Natural Science Foundation for Excellent Young Scientists (no. LR13E050002). This work is also supported in part by the Innovation Project of GUET Graduate Education (no. XJYC2012003), which is very much appreciated.